Inversion of polarimetric data from eclipsing binaries

We describe a method for determining the limb polarization and limb darkening of stars in eclipsing binary systems, by inverting photometric and polarimetric light curves. Because of the ill-conditioning of the problem, we use the Backus-Gilbert method to control the resolution and stability of the recovered solution, and to make quantita- tive estimates of the maximum accuracy possible. Using this method we conrm that the limb polarization can in- deed be recovered, and demonstrate this with simulated data, thus determining the level of observational accuracy required to achieve a given accuracy of reconstruction. This allows us to set out an optimal observational strat- egy, and to critcally assess the claimed detection of limb polarization in the Algol system. The use of polarization in stars has been proposed as a diagnostic tool in microlensing surveys by Simmons et al. (1995), and we discuss the extension of this work to the case of microlensing of extended sources.